{"language":[{"iso":"eng"}],"publisher":"World Scientific","quality_controlled":"1","abstract":[{"lang":"eng","text":"We consider the evolution of a set carried by a space periodic incompressible stochastic flow in a Euclidean space. We\r\nreport on three main results obtained in [8, 9, 10] concerning long time behaviour for a typical realization of the stochastic flow. First, at time t most of the particles are at a distance of order √t away from the origin. Moreover, we prove a Central Limit Theorem for the evolution of a measure carried by the flow, which holds for almost every realization of the flow. Second, we show the existence of a zero measure full Hausdorff dimension set of points, which\r\nescape to infinity at a linear rate. Third, in the 2-dimensional case, we study the set of points visited by the original set by time t. Such a set, when scaled down by the factor of t, has a limiting non random shape."}],"year":"2006","publication_identifier":{"isbn":["9789812562012","9789812704016"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","page":"290-295","status":"public","extern":"1","date_published":"2006-03-01T00:00:00Z","date_created":"2020-09-18T10:48:59Z","publication_status":"published","day":"01","publication":"XIVth International Congress on Mathematical Physics","citation":{"mla":"Kaloshin, Vadim, et al. “Long Time Behaviour of Periodic Stochastic Flows.” <i>XIVth International Congress on Mathematical Physics</i>, World Scientific, 2006, pp. 290–95, doi:<a href=\"https://doi.org/10.1142/9789812704016_0026\">10.1142/9789812704016_0026</a>.","ieee":"V. Kaloshin, D. DOLGOPYAT, and L. KORALOV, “Long time behaviour of periodic stochastic flows,” in <i>XIVth International Congress on Mathematical Physics</i>, Lisbon, Portugal, 2006, pp. 290–295.","ama":"Kaloshin V, DOLGOPYAT D, KORALOV L. Long time behaviour of periodic stochastic flows. In: <i>XIVth International Congress on Mathematical Physics</i>. World Scientific; 2006:290-295. doi:<a href=\"https://doi.org/10.1142/9789812704016_0026\">10.1142/9789812704016_0026</a>","ista":"Kaloshin V, DOLGOPYAT D, KORALOV L. 2006. Long time behaviour of periodic stochastic flows. XIVth International Congress on Mathematical Physics. International Congress on Mathematical Physics, 290–295.","short":"V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–295.","apa":"Kaloshin, V., DOLGOPYAT, D., &#38; KORALOV, L. (2006). Long time behaviour of periodic stochastic flows. In <i>XIVth International Congress on Mathematical Physics</i> (pp. 290–295). Lisbon, Portugal: World Scientific. <a href=\"https://doi.org/10.1142/9789812704016_0026\">https://doi.org/10.1142/9789812704016_0026</a>","chicago":"Kaloshin, Vadim, D. DOLGOPYAT, and L. KORALOV. “Long Time Behaviour of Periodic Stochastic Flows.” In <i>XIVth International Congress on Mathematical Physics</i>, 290–95. World Scientific, 2006. <a href=\"https://doi.org/10.1142/9789812704016_0026\">https://doi.org/10.1142/9789812704016_0026</a>."},"conference":{"end_date":"2003-08-02","start_date":"2003-07-28","name":"International Congress on Mathematical Physics","location":"Lisbon, Portugal"},"type":"conference","author":[{"first_name":"Vadim","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"first_name":"D.","last_name":"DOLGOPYAT","full_name":"DOLGOPYAT, D."},{"full_name":"KORALOV, L.","last_name":"KORALOV","first_name":"L."}],"date_updated":"2021-01-12T08:19:49Z","month":"03","doi":"10.1142/9789812704016_0026","title":"Long time behaviour of periodic stochastic flows","_id":"8515","article_processing_charge":"No"}